Question

2 write an equation in point slope form, slope intercept form, and then in standard form for the following: (-1,7) and a slope of -3. point - slope form: $y - 7 = -3(x + 1)$ slope - intercept form: $y = -3x + 4$ standard form: $-3x + 1y = 4$

Explanation:

Step1: Verify point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$
Substitute $m=-3$, $x_1=-1$, $y_1=7$:
$y - 7 = -3(x - (-1))$
Simplify to $y - 7 = -3(x + 1)$

Step2: Verify slope-intercept form

Expand point-slope form:
$y - 7 = -3x - 3$
Solve for $y$:
$y = -3x - 3 + 7$
Simplify to $y = -3x + 4$

Step3: Verify standard form

Standard form: $Ax + By = C$ (A≥0 preferred)
Rearrange $y = -3x + 4$:
$3x + y = 4$
(Note: $-3x + 1y = 4$ is equivalent, but standard form typically uses a positive leading coefficient)

Answer:

Point-slope form: $\boldsymbol{y - 7 = -3(x + 1)}$
Slope-intercept form: $\boldsymbol{y = -3x + 4}$
Standard form: $\boldsymbol{3x + y = 4}$ (or $\boldsymbol{-3x + y = 4}$ as given, with positive $A$ being the conventional standard)